Problem: $\overline{AB}$ = $52$ $\overline{AC} = {?}$ $A$ $C$ $B$ $52$ $?$ $ \sin( \angle ABC ) = \dfrac{5}{13}, \cos( \angle ABC ) = \dfrac{12}{13}, \tan( \angle ABC ) = \dfrac{5}{12}$
Answer: $\overline{AB}$ is the hypotenuse $\overline{AC}$ is opposite to $\angle ABC$ SOH CAH TOA We know the hypotenuse and need to solve for the opposite side so we can use the sine function (SOH) $ \sin( \angle ABC ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{\overline{AC}}{\overline{AB}}= \frac{\overline{AC}}{52} $ Since we have already been given $\sin( \angle ABC )$ , we can set up a proportion to find $\overline{AC}$ $ \sin( \angle ABC ) = \dfrac{5}{13} = \frac{\overline{AC}}{52}$ Simplify. $\overline{AC} = 20$